997. Find the Town Judge - Explanation

Problem Link

Description

In a town, there are n people labeled from 1 to n. There is a rumor that one of these people is secretly the town judge.

If the town judge exists, then:

1. The town judge trusts nobody.
2. Everybody (except for the town judge) trusts the town judge.
3. There is exactly one person that satisfies properties 1 and 2.

You are given an array trust where trust[i] = [ai, bi] representing that the person labeled ai trusts the person labeled bi.

Return the label of the town judge if the town judge exists and can be identified, or return -1 otherwise.

Example 1:

Input: n = 4, trust = [[1,3],[4,3],[2,3]]

Output: 3

Example 2:

Input: n = 3, trust = [[1,3],[2,3],[3,1],[3,2]]

Output: -1

Constraints:

• 1 <= n <= 1000
• 0 <= trust.length <= 10,000
• trust[i].length == 2
• All the pairs of trust are unique.
• trust[i][0] != trust[i][1]
• 1 <= trust[i][0], trust[i][1] <= n

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1. Indegree & Outdegree

class Solution:
    def findJudge(self, n: int, trust: List[List[int]]) -> int:
        incoming = defaultdict(int)
        outgoing = defaultdict(int)

        for src, dst in trust:
            outgoing[src] += 1
            incoming[dst] += 1

        for i in range(1, n + 1):
            if outgoing[i] == 0 and incoming[i] == n - 1:
                return i

        return -1

Time & Space Complexity

• Time complexity: $O(V + E)$
• Space complexity: $O(V)$

Where $V$ is the number of vertices and $E$ is the number of edges.

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2. Indegree & Outdegree (Optimal)

class Solution:
    def findJudge(self, n: int, trust: List[List[int]]) -> int:
        delta = defaultdict(int)

        for src, dst in trust:
            delta[src] -= 1
            delta[dst] += 1

        for i in range(1, n + 1):
            if delta[i] == n - 1:
                return i

        return -1

Time & Space Complexity

• Time complexity: $O(V + E)$
• Space complexity: $O(V)$

Where $V$ is the number of vertices and $E$ is the number of edges.